Occupation-selective topological pumping from Floquet gauge fields

Abstract

Topological pumping is conventionally governed by single-particle band topology. Here we show that promoting tunneling to a dynamical, occupation-conditioned variable fundamentally reshapes this paradigm, leading to occupation-selective topological pumping. In a periodically driven one-dimensional superlattice with density-dependent hopping, two-body bound states (doublons) acquire Chern numbers distinct from those of single particles and exhibit quantized transport even when the single-particle pump is trivial, including counter-propagating responses. We identify a dynamical-gauge-field mechanism that induces topological phase transitions in the bound-state sector absent from the single-particle spectrum. Furthermore, the gauge field concentrates Berry curvature into sharply localized resonant regions without compromising adiabatic quantization. A Floquet realization with ultracold atoms is proposed to realize such occupation-selective pumping. Our results reveal a mechanism for occupation-selective topological responses that can persist across higher-occupancy bound states.

Figures (9)

• Figure 1: Schematic illustration of occupation-selective topological pumping beyond the single-particle paradigm. (a) Occupation-unselective pumping without a dynamical gauge field: in the conventional Thouless pump, single particle moves one unit cell over a cycle [$\phi = 0$ (blue circle) $\to$$\phi = 2\pi$ (red circle)], and doublon follows the same path. (b) Occupation-selective pumping via a dynamical gauge field: density-dependent tunneling renders the hopping amplitude dynamical, allowing the pumping response to depend on particle occupation. (b1) Topology-enabled doublon pumping: doublon exhibits quantized transport even when the single-particle pump is topologically trivial, whose dynamical realization is shown in Fig. \ref{['fig:DensityEvolution']}(a). (b2) Counter-propagating pumping: the pumping directions experienced by single and double-boson state sectors can be opposite, with the corresponding dynamics illustrated in Fig. \ref{['fig:DensityEvolution']}(b).
• Figure 2: Topological characterization and response of the doublon bound-state band. Dynamical-gauge-field–induced Berry curvature and quantized polarization of the lower two-body bound-state band for different density-dependent hopping amplitudes $\gamma_0$. Columns (a)--(c) correspond to $\gamma_0=3.5$, $0$, and $-1.5$, respectively. Upper row: Berry curvature $\mathcal{F}_{d}$ in the $(\phi,k)$ parameter space. The curvature exhibits extremely sharp, localized peaks and valleys, leading to a highly discontinuous appearance in the linear color scale. These sharp local features are a consequence of the dynamical gauge field and do not affect the global topological properties. Lower row: Variation of the polarization $P_{d}$ over one driving period (left axis) and the minimum energy gap $\Delta_{\min}$ between the two bound-state bands after scanning the Brillouin zone (right axis). The sharp transitions in $P_{d}$ reflects a dynamical-gauge-field–enhanced resonant switching of the Wannier center. A quantized winding of $P_{d}$ is observed for $\gamma_0=3.5$ and $-1.5$, corresponding to $C_d=+1$ and $-1$, respectively, while no winding occurs for $\gamma_0=0$, indicating a topologically trivial phase.
• Figure 3: Dynamical-gauge-field–induced doublon topology beyond the single-particle phase diagram. (a) Chern number $C_d$ of the lower doublon band in the $(\gamma,\gamma_0)$ plane, with $\gamma$ (static) and $\gamma_0$ (dynamical gauge-field) intra-cell hopping. The gray shaded region indicate the corresponding single-particle topology $C_{s}=-1$; along the density-independent limit $\gamma_0=0$ (red dashed line), the doublon topology follows that of the single-particle one. For $\gamma_0\neq0$, the dynamical gauge field generates topology unique to the doublon sector, including $C_{d}=\pm1$ even when $C_{s}=0$, establishing occupation-selective topology. (b)–(d) Pumping trajectories in the effective parameter space $(\widetilde{\Delta}(\phi),\widetilde{J}(\phi))$ at fixed $\gamma=2$ for $\gamma_0=3.5,0,-1.5$. The red dot marks the band-touching point. As $\gamma_0$ is tuned away from zero, the trajectory evolves from not enclosing to encircling this degeneracy, directly revealing a dynamical-gauge-field–driven topological phase transition from trivial to nontrivial winding, with opposite circulation corresponding to opposite signs of $C_{d}$.
• Figure 4: Dynamics of dynamical-gauge-field-induced occupation-selective topological pumping. The phase $\phi(t)$ is driven according to Eq. (\ref{['DrivenFrequency']}), where the driving frequency is chosen to ensure an adiabatic evolution over one pumping cycle. (a) Topology-enabled doublon pumping $(\gamma = 2,\ \gamma_0 = 3.5)$. Time evolution of the site-resolved density for a single particle (a1) and for a two-particle bound state (doublon) (a2) over one pumping cycle, with color indicating the renormalized occupation $\bar{n}_j$. Although the single-particle pump is topologically trivial, the doublon undergoes quantized transport. The resulting center-of-mass displacement $\Delta X/2$ is shown in (a3), where solid red and dashed blue curves denote the single- and double-occupancy sectors, respectively. (b) Counter-propagating occupation pumping $(\gamma = 0.5,\ \gamma_0 = 2)$. The same quantities are shown in (b1)--(b3), demonstrating that the single- and double-occupancy sectors are pumped in opposite directions under the same adiabatic driving protocol.
• Figure S1: Full two-particle energy spectrum underlying the topological analysis in the main text. Panels (a)–(c) correspond to different values of the density-dependent hopping amplitude $\gamma_0$, which acts as the strength of the dynamical gauge-field–mediated tunneling. Throughout the driving cycle, the scattering continuum remains clearly separated from two isolated bound-state bands. We focus on the lower bound band and denote its Chern number by $C_d$, as indicated in each panel. Tuning $\gamma_0$ modifies the effective intra-cell tunneling of the doublon and drives a topological transition, with $C_d$ changing from $+1$ to $-1$ as $\gamma_0$ varies from $3.5$ to $-1.5$.